Subject Index for E. T. Jaynes : Probability Theory			Prepared by Arnold Baise, May 2010						Updated June 2017.
a priori probabilities	87
ad hoc/hockery	xxiii	xxviii	4	9n	22	47	117	135	137	140	143	154n	174n
	179	217	239n	243	252-53	264	346	397	432	467	469	484-85	488
	492	508	510	534-35	551-52	562	574	616-18	649	673	699	708
additive measure	48	262	270	653	657
additivity	97-98	652-54	656
countable	464-66
finite	xxi	464-67	485
adequate set	12	15-16	35	652
admissible/inadmissible	408-09	415	419	438	508	526	618n	718
ancillarity	212n	252-54
ancillary statistic/information	xxiii	253-56	497	510	550-51
Ap distribution	9	553-88
Aristotelian logic/propositions	9	13	16	23	30	35	45n	146n	554	560	652	661
(see also non-Aristotelian)
autoregressive model	80	125
average sample number (ASN)	106
backward inference	62	80-81
barber paradox	673
Bayes theorem	112
and ancillarity	253-56
and Ap distribution	554-56
and converging views	129-32
and decision theory	413-18
and discovery of Neptune	134-39
and model comparison	604-07
and R.C. Jeffrey	140-43
and significance tests	293-99	300-05
and sufficiency	246-50
Bernoulli
Ars Conjectandi	xx	82
class	121	297-98	300	305
trials	164	166	382	385
urn	42	51-52	59-60	67	73	153	496
Bertrand's problem	386-96
beta
distribution	189	199
function	112	115	563
binomial distribution	69-71	75-76	79	83	95	105	111	120-22	155-56	160	162-63	169-70	199
	204	243	248	278	284	294	301	330	365	462	467	531	562
	578	648
Blackwell-Rao theorem	247-48
Boolean algebra	9-11	23	26	34-35	48	59	62	64	66	101	107	166	249
	369	464	652	654	661
Borel field	628	676
Borel-Kolmogorov paradox	110-11	467	487	654
Bose-Einstein statistics	285	447
bridge hands	321-23
Carnap inductive methods	279	574
Cauchy distribution	212n	218	224	248	502	503n	551	600
Cauchy theorem	569
causal versus logical independence	4-5	83-84	88	91-92	98	118	162-64	169	258	260	266	285	585
	695
censored data	164n	168
central limit theorem	199	204	206	209	221-26	242	437	448	532	592	610
and computation accuracy	224
change-point problem	474
characteristic function	223-24
Chauvenet criterion	616
Chebyshev inequality, see Tchebycheff
chi-squared
distribution	284	303
test	122	135	284	299	300-05	394	495n	523n	534	581
coherence	372	425	655-56
coin tossing	61n	82	164	251-52	268	277-79	300-01	317-21	329-39	398-99	553	573-74
communication theory	627
encoding	638
with digram frequencies	641
history	521n	627-28
and Markov chain	645	647
and maximum entropy	365
noiseless channel	628-34
noisy channel	648
complete class theorem	408	412	415
complete ignorance	113	181-83	284	373-74	377-79	381	383-85	395-96	478-80	484-85	573	575	694
conditionality principle	251-52
confidence intervals	xxiii	241	377	385	492	495n	510	576-77	583-85	673-74	674n	695	698
conglomerability	453-54	457
convergence/divergence of opinions	126-32
convolution	205	221-23	227	236	242	522	667	677-79
correlation	75-77	79-81	125	137	207	207n	215	226	267	285	288	330	387
	529	534-35	584	609	641
coefficient	467	494	538	545
countable additivity	464-66
covariance	361-62
matrix	215	546-49
Cox theorems	xx	xxiii	45	47	65	98	108	111	117	133	143	252	264
	301	418	486	488	508-09	562	619	657	662	668
Cramér-Rao inequality	412	518
cumulants	222	362	677-81
Darwin-Fowler method	441	631
Darwinian evolution	132-33	229-32	312	316	561
de Finetti
coherence	372	425	655-56
exchangeability theorem	317	337	586-88	620	655
de Moivre-Laplace limit theorem	113	189	290	292
decibels	91-93	117	294	296-98
decision theory
criterion
Bayes	431-33
maximin	436
minimax	407	431	435-36
minimin	407
and inference	397-98	405-07
loss function	400	407	409-24	430-38
Neyman-Pearson	432	436-38
and objectivity	418-21
Wald	406-09	421	424	438
widget problem	440-50
delta function	108	111-12	186n	189	223	223n	238	253	410	520	668-70
desideratum/desiderata	9	16-17	19	22	24-26	29-30	34	37	39-41	44-45	51	73	86-87
	127	140	143	146n	166	182	210	217-18	244	248n	264-65	335	369
	379	382	388-89	391	418	423	507	528	651	656-57	662
detrending/seasonal adjustment	xxvii	535-49
disjunctive normal form	15	34
distribution
Ap	9	553-88
beta	189	199
binomial	69-71	75-76	79	83	95	105	111	120-22	155-56	160	162-63	169-70	199
	204	243	248	278	284	294	301	330	365	462	467	531	562
	578	648
Cauchy	212n	218	224	248	502	503n	551	600
chi-squared	284	303
exchangeable	62	77	80-81	137
Gaussian	113	189	198-99	200-21	225-41	243	246	448	498	501-02	513	527-30	537
	550-51	592-94	596	600	610	625	680
bivariate	467	479	491	550
derivation
Gauss	202-04	220	241
Herschel-Maxwell	200-01	204	529
Landon	205-06	206n
multivariate	493-94
hypergeometric	56-59	62	68-71	83-84	150	152-53	159	278-79	563
multinomial	71	284	351-52	578	640
Poisson	170-71	185	189	284	294-95	304	382	516	518
predictive	154	498
pseudoposterior	479	485
rectangular	190-91	225	243	248
sampling	xxivn	xxviii	84-85	88-89	94	164
Student's t	551
uniform	179	204	291	322	331	338	386	466	470
divergence/convergence of opinions	126-32
DSZ (Dawid, Stone & Zidek)	470-84	488
economics	199	208n	233	267n	505	510	514	520	534-35
efficient estimator	377	412	520n
Emperor of China fallacy	258	337
entropy	121-22	221	232n	234	247n	257	285-91	298	346	351	364	371	375
	402-04	429-30	480	484	627	634	644
concentration theorem	353n	630	632
maximum	xxiii	xxiv	88	94n	141	206n	208	216-17	217n	232n	241-42	287n	288
	290-92	335	351	353-56	358-74	376-77	396	426	437	440-41	444	446	450
	519-20	534	544	563-64	576-77	592	595	602n	610	614	632	638-39	641
	647	655
estimator	172-74	247-48	252-53	253n	254n	410-14	417	423	493-94	500-03	507	507n
	510	514n	533	551	600
Bayesian	516	536-41	544-45
efficient	377	412	520n
maximum likelihood (MLE)	175-76	175n	180	182	202	204	211-12	211n	416	575	604	609
optimal	xxiii	172	212	412-13	416-17	501	540-42
robust	174	618	618n
unbiased	377	412	492	495n	508	510-19	520n	534	541	670
unbiased minimum variance (UMV)	412	520
Eulerian
angle	332	333n
integral	112	165	563
evolution, Darwinian	132-33	229-32	312	316	561
exchangeability	64	81	292
theorem	317	337	586-88	620	655
exchangeable
distribution	62	77	80-81	137
prior	620
sampling	244
sequence	125	292	337	344	576	586	588	640
extrasensory perception (ESP)	119-26	128	133	140
fallacy
Emperor of China	258	337
mind projection	22-23	74-75	83	92	108	113	131	212n	316	411	500	506	526n
	552	601	609	628
sample-reuse	264-66
finite additivity	xxi	464-67	485
Fisher information	256-57
Fisher, Sir Ronald
collected works	495
and H. Jeffreys	293	316	484n	493-99	568	604
and K. Pearson	303n	495	495n
Statistical Methods for Research Workers	492
fluctuation-dissipation theorems	232
Fokker-Planck equation	206n	207
Fourier
analysis	223n	536	552	668
Dirichlet form	667
series	226	587	667	669-70
transform	xxvii	125	221-23	235-36	238	521-22	667-68	678	680
Fredholm integral equation	482
frequentist probability	xxii	xxiii	75	270	280	284	289	314-15	334	336	339	404	411
	508	576	579	583	635
functional equation	25-33	45	65	201	224	347-48	351	353	379-82	384	389-90	396	486
	653	668
gambler's ruin	402
Gaussian
distribution	113	189	198-99	200-21	225-41	243	246	448	498	501-02	513	527-30	537
	550-51	592-94	596	600	610	625	680
noise	208	214	217	255	433	437	439-40	523	545
generalized
ancillary information	254-55
inverse problem	50	175n	239	595
sufficiency	248
Gibbs
algorithm	290-91
canonical ensemble	292	370-71
grand canonical ensemble	371	447
inequality	291
thermal equilibrium	232n	291
Gödel
incompleteness	7	16
theorem	12	45-47	83	350	423
great inequality of Jupiter and Saturn	203	234	589
group invariance	40	88	332	423	480
group theory	332	335	378	673n
Haar measure	49	378
Haldane prior	166	575
Hamiltonian	614
Hanbury Brown-Twiss interferometer	207n
Hausdorff
moment problem	587
sphere paradox	672-74
Hempel paradox	143-44	486	488	691
Hermite polynomials	236
Hilbert space	249	483
Hurwitz invariant integral	49
Huygens principle of optics	141	428
hypergeometric distribution	56-59	62	68-71	83-84	95	150	152-53	159	278-79	563
hypothesis testing	61-62	86-118	149	163	250	253	305	310	343	404	418	491-92	606n
	625	711
iid	212	526	526n
implication
logical	11-13	45n	132n
logical vs causal	4-5	61
improper prior	160	165-66	415	471-81	485	487-88
independence
logical	97	111	136	162-63	177	185	226	264-65	277	514	653
logical vs causal	83-84	88	91-92	98	118	162-64	169	258	260	266	285	585
indifference, principle of	40	51	94	262	274	331-32	338	343	353	386-87	394-95	418	564-65
	571	573
induction
mathematical	38	77	79	223	349
inferential	155	270	276-80	310-12	326	499
reverse	278-79
inductive reasoning	xix	45n	208	277-79	284	311	314	323	325-26	335	339	370-71	377
	383	386	491	499	521	557	571	573-74	585	600	660
infinite
population	82-83	498
regress	252	324-25	439
sets	xxii	21	43-44	108-09	451-53	456	458-59	462	464-66	485-87	652	663-64	671-74
insurance	400-02	404	421	578
interval estimation	149	163	168	186	250	253	385	550	698
invariant measure	333	375	378	396
jackknife	174n
Jacobian	244	266	379	392	468
Jeffreys prior	181-83	186	377	380-81	395	423	476	478	481-82	498	530
Jeffreys, Sir Harold
and R.A. Fisher	293	316	484n	493-99	568	604
and J. Neyman	293	316	496-99
limb-sawing reasoning	524
Jupiter and Saturn, great inequality	203	234	589
Kolmogorov system	49	651-55
Kullback-Leibler information	403
Lagrange multiplier	346	354-56	358	376	443	446	520	631	639	643
Lagrangian	331	334
Laplace
Essai Philosophique sur les Probabilités	124	591	596
rule of succession	155	158	165	209	279	292	321	339	383	385-86	563-68	571	574-81
	588
transform	281	477	569-70	577
lattice theory	657	659
law of large numbers	74-75	292	336-37	353
least squares	xxviii	172	175	299	539-42	591-92	595	609	611-12
Lebesgue measure	44	663
Lebesgue-Stieltjes
integral	628
notation	112
Legendre
polynomials	545	587
transformation	359-60	364
likelihood	xxviii	89	121	166	178	178n	183	191	213-14	216	250	255	263
	265	267	314	480	482-83	487-88	494	507	526	538	545	602	604-05
	607	625
asymptotic	256-57
log	91	129	256	532-33
maximum	xxviii	121	175-76	175n	180	182	195	202	204	211-12	316	414	416
	492	495n	510-11	575	594-95	603-05	607	609	611
principle	250-54	505	603
quasi-	529-30	622-24
ratio	90-91	122	138	265	433	556	610	612
limit theorems	74-75	284-85	330	337	337	515
linear regression	497	541-42	551
Liouville's theorem	232n	333
logic
Aristotelian	9	13	16	23	30	35	45n	146n	554	560	652	661
non-Aristotelian	16	146n	601
logical vs causal independence	4-5	83-84	88	91-92	98	118	162-64	169	258	260	266	285	585
	695
logit	116
Lorentz transformation	201
loss function	400	407	409-24	430-38
quadratic	376	385	411	413	512	539	600	625
magnification	300	534
marginal
posterior distribution	150	219	250	471	475	481	483-85	537-38	548	622
distribution	215	244-45	256	467-68	473	485	539
utility	399
marginalization paradox	55	144	166	219	244	458	470	479	484	486-88	565n	662
Markov chain	77	80	460	645	647
maximum entropy	xxiii	xxiv	88	94n	141	206n	208	216-17	217n	232n	241-42	287n	288
	290-92	335	351	353-56	358-74	376-77	396	426	437	440-41	444	446	450
	519-20	534	544	563-64	576-77	592	595	602n	610	614	632	638-39	641
	647	655
maximum likelihood	xxviii	121	175-76	175n	180	182	195	202	204	211-12	316	414	416
	492	495n	510-11	575	594-95	603-05	607	609	611
estimator (MLE)	175-76	175n	180	182	202	204	211-12	211n	414	416	575	604	609
Maxwell
demon	207n
distribution	201	241	494
measure
additive	48	262	270	653	657
invariant	333	375	378	396
theory	44	109	628	663-65	674
meta-analysis	258	260-61	266
mind projection fallacy	22-23	74-75	83	92	108	113	131	212n	316	411	500	506	526n
	552	601	609	628
missing data	533-34
model comparison	601
Monte Carlo integration	531-32
moving average	521-22	522n	523	671n
multinomial distribution	71	284	351-52	578	640
Murphy's law	203
Neptune, discovery of	133-35	137-39
Neyman-Pearson theory	404	426	432	436-38	492	510-11
non-Aristotelian logic/propositions	16	146n	601
nonconglomerability	xxi	453-59	464	479	485-86	664
notation, probability	17-18	43	55	178	554	661-62
nuisance parameter	xxiii	xxviii	115	118	167	195	209	219-20	249-50	261	316	344	456
	470-71	475	479	482	484	497	502	527-29	535	537-38	542-44	547	550-51
	606	621	673
Nyquist
frequencies	521	523
law	205n	208-09	232
noise	209	363	521n	609
objective/objectivity	44-45	61n	86	196	334	358	373	393	411	418-20	424	480	484n
	493	498	500	515n	550	639	658
Ockham
factor	603-05	607	610-13
razor	601	606	613
odds	57	90	90n	92-93	97	106	309	366	557
log	91	97	116	129	166	602n
posterior	90	438	461-63
ratio	122	138	144	552	602-04
ontological vs epistemological	22
optimal estimator	xxiii	172	212	412-13	416-17	501	540-42
optional stopping	96	166-67
orthodox statistics	490	509
outliers	615-17	620-26
P-value	304	523
paradox	44	451
barber	673
Borel-Kolmogorov	110-11	467	487	654
great circle	470
Hausdorff sphere	672-74
Hempel	143-44	486	488	691
marginalization	55	144	166	219	244	458	470	479	484	486-88	565n	662
reduction principle	472	477-79	484-85
nonconglomerability	xxi	453-59	464	479	485-86	664
pooling data	219	260-61
Simpson, see pooling data
St Petersburg	398-99	400	404
tumbling tetrahedra	456-64	488
parameter
estimation	118	149-97	215	266	305	410	491-92	523n	533	576-77	603
nuisance	xxiii	xxviii	115	118	167	195	209	219-20	249-50	261	316	344	456
	470-71	475	479	482	484	497	502	527-29	535	537-38	542-44	547	550-51
	606	621	673
of location	202	215	220	253	378	491	530	533	625
of scale	202	205	378	423	474	491	498	530	694
partition function	281-83	289-91	354	356	362	364	376	443	446	602n	631	633	639
	641-42	645
periodogram	523	524n
Pitman-Koopman theorem	247n	519
Planck radiation law	209
Poisson distribution	170-71	185	189	284	294-95	304	382	516	518
pooling data paradox	219	260-61
predictive distribution	154	498
predictive probability	155	165	463
Principia Mathematica	306	561
principle of indifference	40	51	94	262	274	331-32	338	343	353	386-87	394-95	418	564-65
	571	573
prior
binomial	160-62	249
concave	158-60	165
data dependent	266
Dirichlet	125
Haldane	166	575
ignorance	374
improper	160	165-66	415	471-81	485	487-88
Jeffreys	181-83	186	377	380-81	395	423	476	478	481-82	498	530
noninformative	40	550
truncated uniform	157
uniform	112	115	152-53	156-60	162	165	181-83	288	316	331	344-45	365-67	373
	377	383	385-86	395	419	423	454	457	479	501	517	528	568
	593	596
uninformative	152	159	182	470	473n	476	478-79	481-85	502	530	533	674
probability
and bridge hands	321-23
as frequency vs information	198	270	292-93	336	388	411	635
frequentist	xxii	xxiii	75	270	280	284	289	314-15	334	336	339	404	411
	508	576	579	583	635
notation	17-18	43	55	178	554	661-62
propensity	60-61	61n	76	327
psi test	300-05	523n
quadratic loss function	376	385	411	413	512	539	600	625
quadratic risk	247-48
quantum
theory	22-23	61n	92	232n	312n	327-30	371
statistics	292	445	447
Radon-Nikodym
derivative	676
theorem	628
random
experiment	xxiii	220	270-71	293	300	314-17	321-25	334-37	353	366	370	374	394
	409	457	495	561	568	572	576	585	653
variable	xx	xxii	314	317-18	372	409	493	500	525	538	551-52	606
walk	106	459
randomization	73-74	252	266	271	467	495n	497n	510	531-32
randomness	xx	74	117	250	271n	314	319	322	423	491	500	552
rectangular distribution	190-91	225	243	248
redescending psi function	174n	621
reduction principle	472	477-79	484-85
Riemann
integral	376	531
geometry	377
Riemann-Lebesgue lemma	238
robot	8-9	12	17-20	22	25	27	29	37	39-42	44	46	51-54	56-57
	59-60	63-64	66	72-73	75	86-87	90-94	94n	95-96	99	102-05	112-15	119
	121-22	150-51	154	166	171-72	176	182	191	208	218-20	267	272-78	283-85
	288-90	336-37	339	343-47	350	355	364	366	369	397-98	406-09	437-39	553-60
	574	584	600	655-56
poorly informed	273-74	276-78	283-85	289-90	337	339
robust/robustness	174	174n	617-18	618n	619	621-22	625
rule of succession	155	158	165	209	279	292	321	339	383	385-86	563-68	571	574-81
	588
Russell
barber paradox	673
Principia Mathematica	306	561
theory of types	560	673
sample re-use fallacy	264-66
sampling distribution	xxivn	xxviii	84-85	88-89	94	164
Schwarz inequality	518	520	543	670
seasonal adjustment/detrending	xxvii	535-49
sequential testing	96-99	100-06	131	272	397
Shannon's theorem	298	346-50	375
Wallis derivation	351-53
significance test	xxiii	71	84-85	118	136-37	293	303	405	423	426	492	495n	504n
	505	510	521	523n	524-25	581	601
Simpson paradox, see pooling data paradox
St Petersburg game	398-99	400	404
statistical mechanics	xxiv	60	80	141	199	201	206n	232	241	285n	290-91	328-29	333
	354	364-65	370-71	428	441	444	450	529	585	602n	609	627	631-32
	638	653	664	670
quantum	292	445	447
Stirling approximation	121	286	352	629	631
stochastic vs deterministic	505-06
strong inconsistency problem	456	463
subjective Bayesian	372-73
subjective/subjectivity	44	61n	372-73	393	420-21	493	515	550
succession, rule of	155	158	165	209	279	292	321	339	383	385-86	563-68	571	574-81
	588
sufficiency	212n	243	245-47	247n	248-51	428-30	519
sufficient statistic	xxiii	213	217n	245-47	247n	248-49	316	429-31	459	461	464	480-81	484
	497	501-02	510	516	520	532	537	550	673
sure thing hypothesis	195	195n	296
syllogism	4-6	8	12	23	35-36	132	134
taxicab problem	190
Taylor series	516	572
Tchebycheff inequality	186	186n
telepathy	120-21	124
thermodynamics	42	146	351	364-65	445	527n	602
second law	209	232	232n
time series	521-22	522n	534-36	671n
Bayesian method	536-49
transformation equations	39-40
transformation group	182	292	378	380-81	383	385-89	392-93	395-96	420	423	555	575-77
tumbling tetrahedra paradox	456-64	488
Turing machine	7	16
unbiased estimator	377	412	492	495n	508	510-19	520n	534	541	670
unbiased minimum variance estimator	412	520
uniform distribution	179	204	291	322	331	338	386	466	470
uniform prior	112	115	152-53	156-60	162	165	181-83	288	316	331	344-45	365-67	373
	377	383	385-86	395	419	423	454	457	479	501	517	528	568
	593	596
uninformative prior	152	159	182	470	473n	476	478-79	481-85	502	530	533	674
unit root	228	228n	233	701
utility	322	399	400-04	420	424
and entropy	402
marginal	399
Venn diagram	47-49	262	651	654
visual perception	132-33	561
Wald
decision theory	406-09	421	424	438
complete class theorem	408	412	415
maximin utility	407
Weber-Fechner law	92-93	95
widget problem	440-50
Wiener-Khinchin theorem	207